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| viXra.org > General Mathematics > 2207 |
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[6] viXra:2207.0127 [pdf] submitted on 2022-07-20 12:53:12
Authors: Edgar Valdebenito
Comments: 13 Pages.
In this note we study the function f(z)=1/(1-2z-z^2-z^4), z complex.
Category: General Mathematics
[5] viXra:2207.0123 [pdf] submitted on 2022-07-19 08:41:02
Authors: Juan Elias Millas Vera
Comments: 17 Pages.
This paper shows information for people who are interested in symbology and its applications. In a very didactic way it puts some of the necessary tools for the knowledge of the different number systems, using the multiplication tables. This paper go around Cuneiform, Old Egyptian, Classical Greek, Hebrew, Roman, Chinese Simplified, Binary, Hexadecimal and of course Eastern Arabic numerals.
Category: General Mathematics
[4] viXra:2207.0083 [pdf] submitted on 2022-07-11 23:47:46
Authors: Temur Z. Kalanov
Comments: 9 Pages. (Corrections made by viXra Admin to conform with scholarly norm - Please conform!)
The critical analysis of the starting point of the theory of complex numbers is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) the definition of a complex number contradicts to the laws of formal logic, because this definition is the union of two contradictory concepts: the concept of a real number and the concept of a non-real (imaginary) number - an image. The concepts of a real number and a non-real (imaginary) number are in logical relation of contradiction: the essential feature of one concept completely negates the essential feature of another concept. These concepts have no common feature (i.e. these concepts have nothing in common with each other), therefore one cannot compare these concepts with each other. Consequently, the concepts of a real number and a non-real (imaginary) number cannot be united and contained in the definition of a complex number. The concept of a complex number is a gross formal-logical error; (2) the real part of a complex number is the result of a measurement. But the non-real (imaginary) part of a complex number is not the result of a measurement. The non-real (imaginary) part is a meaningless symbol, because the mathematical (quantitative) operation of multiplication of a real number by a meaningless symbol is a meaningless operation. This means that the theory of complex number is not a correct method of calculation. Consequently, mathematical (quantitative) operations on meaningless symbols are a gross formal-logical error; (3) a complex number cannot be represented (interpreted) in the Cartesian geometric coordinate system, because the Cartesian coordinate system is a system of two identical scales (rulers). The standard geometric representation (interpretation) of a complex number leads to the logical contradictions if the scales (rulers) are not identical. This means that the scale of non-real (imaginary) numbers cannot exist in the Cartesian geometric coordinate system. Consequently, the theory of complex numbers and the use of the theory of complex numbers in mathematics and physics (electromagnetism and electrical engineering, fluid dynamics, quantum mechanics, relativity) represent a gross methodological error and lead to gross errors in mathematics and physics.
Category: General Mathematics
[3] viXra:2207.0078 [pdf] submitted on 2022-07-10 23:59:37
Authors: Edgar Valdebenito
Comments: 3 Pages.
Solving quartics via Ferrari's method.
Category: General Mathematics
[2] viXra:2207.0053 [pdf] submitted on 2022-07-06 20:28:23
Authors: Temur Z. Kalanov
Comments: 20 Pages. (Corrections made by viXra Admin to conform with scholarly norm)
The critical analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and rational dialectics is methodological basis of the analysis. The analysis leads to the following main results: (1) trigonometry does not treat a right triangle as a material system. Therefore, trigonometry does not satisfy the system principle; (2) trigonometric functions do not satisfy the mathematical definition of a function. The terms “sine”, “cosine”, “tangent”, “cotangent” and others are not identical to the concept of function. Symbols “cos”, “sin”, “tg”, “ctg”, etc. indicate only that there is a correspondence (connection) between the values of the quantities of the angle and the lengths of the sides in a right-angled triangle. Therefore, the standard definitions of trigonometric functions do not represent mathematical (quantitative) relationships between the quantities of the angle and the lengths of the sides in a right-angled triangle. Trigonometric functions are neither explicit nor implicit functions; (3) the range of definition of trigonometric functions does not satisfy the condition for the existence of a right-angled triangle because the definitions of trigonometric functions contradict to the system principle. These facts prove the assertion that the trigonometric functions, the trigonometric identities, the trigonometric form of the Pythagorean theorem and the inverse trigonometric functions are blunders; (4) the values of mathematical quantities are always neutral numbers. Therefore, logical contradictions arise if the quantity of the angle and the symbols “cos”, “sin”, “tg”, “ctg” take on negative values. (5) it is proved that the standard theorems of addition (difference) of two arguments for cosine and sine are blunders. This means that the addition (difference) theorems for all trigonometric functions, the reduction formula, the formula for double and half argument are blunders; (6) in the point of view of the Cartesian coordinate system, the abscissa and ordinate scales are identical and have the dimension “meter”. Therefore, the quantity of the angle (which has the dimension “degree”) does not exist in the Cartesian coordinate system; (7) the graphs of trigonometric functions are built in an inadmissible coordinate system because the scales are not identical: the abscissa scale has the dimension “degree”, and the ordinate scale has the dimension “meter”. The non-identity of the dimensions leads to absurdity: “meter” is “degree”. Therefore, the graphs of trigonometric functions have no geometric meaning; (8) if the material point is the end point of the moving radius in the material system “circle + mobile radius + Cartesian coordinate system”, then the graph of the dependence of the ordinate of the material point on the length of the path traveled (i.e., on the circumference of a given radius) has the form of a sinusoid, but the graph is not a trigonometric sinusoid.
Consequently, standard trigonometry is a pseudoscientific theory.
Category: General Mathematics
[1] viXra:2207.0025 [pdf] submitted on 2022-07-04 22:42:27
Authors: Michele Nardelli, Antonio Nardelli
Comments: 143 Pages.
In this paper, we analyze further Ramanujan’s continued fractions. We describe the new possible mathematical connections with the MRB Constant and various equations concerning the Dirichlet L- functions and some sectors of String Theory
Category: General Mathematics
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